Overtone scale: Difference between revisions

Line 146:

===Over-p scales===

[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls ''primodal scales''. To construct a primodal scale, we fix a prime p to be the denominator and take intervals of the form n/p, where n ≥ p. Zhea often takes n to range over a certain "lineal segment" (a segment of the harmonic series spanning an octave starting from mp where m is a positive integer) or a subset thereof. For example, if we use p = 13 and and take all n between 13 and 26 (inclusive), this would result in the scale ~~1/1,~~ 14~~/13,~~ 15~~/13,~~ 16~~/13, ...,~~ 24~~/13,~~ 25~~/13, 2/1~~. We may add a 3/2 to the scale root, which corresponds to adding 3p/p.

[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls ''primodal scales''. To construct a primodal scale, we fix a prime p to be the denominator and take intervals of the form n/p, where n ≥ p. Zhea often takes n to range over a certain "lineal segment" (a segment of the harmonic series spanning an octave starting from mp where m is a positive integer) or a subset thereof. For example, if we use p = 13 and and take all n between 13 and 26 (inclusive), this would result in the scale 13:14:15:16:17:18:19:20:21:22:23:24:25:26. We may add a 3/2 to the scale root, which corresponds to adding 3p/p.

Primodality seems designed to emphasize the identity of the "tonic" as the pth harmonic; this may help in hearing higher primes such as 17, 19, and 23 which may be difficult to hear otherwise as the overtone of some fundamental.

@@ Line 146: / Line 146: @@
 ===Over-p scales===
-[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls ''primodal scales''. To construct a primodal scale, we fix a prime p to be the denominator and take intervals of the form n/p, where n ≥ p. Zhea often takes n to range over a certain "lineal segment" (a segment of the harmonic series spanning an octave starting from mp where m is a positive integer) or a subset thereof. For example, if we use p = 13 and and take all n between 13 and 26 (inclusive), this would result in the scale 1/1, 14/13, 15/13, 16/13, ..., 24/13, 25/13, 2/1. We may add a 3/2 to the scale root, which corresponds to adding 3p/p.
+[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls ''primodal scales''. To construct a primodal scale, we fix a prime p to be the denominator and take intervals of the form n/p, where n ≥ p. Zhea often takes n to range over a certain "lineal segment" (a segment of the harmonic series spanning an octave starting from mp where m is a positive integer) or a subset thereof. For example, if we use p = 13 and and take all n between 13 and 26 (inclusive), this would result in the scale 13:14:15:16:17:18:19:20:21:22:23:24:25:26. We may add a 3/2 to the scale root, which corresponds to adding 3p/p.
 Primodality seems designed to emphasize the identity of the "tonic" as the pth harmonic; this may help in hearing higher primes such as 17, 19, and 23 which may be difficult to hear otherwise as the overtone of some fundamental.